A367649 Primes p such that the multiplicative order of 3 modulo p is 2 times a power of 3.

7, 19, 37, 163, 487, 1297, 1459, 2917, 19441, 19927, 39367, 59779, 131221, 208657, 224209, 572023, 2051893, 5062663, 8503057, 19131877, 44457337, 86093443, 113863969, 133923133, 258280327, 565571323, 600830137, 859270843, 1319934691, 4161183031, 5366491219, 5879415781

Offset: 1

Author

Jianing Song, Nov 25 2023

Keywords

• nonn

Comments

Odd prime factors of numbers of the form 3^3^i + 1: for odd primes p, p divides 3^3^i + 1 if and only if the multiplicative order of 3 modulo p is 2 times a power of 3 not exceeding 3^i.

Examples

			37 is a term since the multiplicative order of 3 modulo 37 is 18 = 2*3^2, which means that 37 is a factor of 3^3^2 + 1.
163 is a term since the multiplicative order of 3 modulo 163 is 162 = 2*3^4, which means that 163 is a factor of 3^3^4 + 1.
		

Crossrefs

Subsequence of A367266.

Cf. A023394 (ord(2,p) being a power of 2, prime factors of numbers of the form 2^2^i - 1 (or of the form 2^2^i + 1)), A367648 (ord(3,p) being a power of 3, prime factors of numbers of the form 3^3^i - 1).

Programs

PARI

isA367649(n) = my(d); isprime(n) && (n!=3) && ((d=znorder(Mod(3,n)))%2==0) && isprimepower(3*d/2)

Extensions

a(28)-a(31) from Chai Wah Wu, Nov 26 2023

a(32) from Jinyuan Wang, Jan 29 2025